From German Patent Disclosure Document DE-OS 32 37 961.7-27, a web-fed offset rotary printing machine is already known which has a number of printing units of the above-specified type disposed in succession in it. If the two middle cylinder, as a rule the rubber blanket cylinders, of such printing units are to be separated from one another, for instance in order to fasten new blankets onto them, then at least one of the outer cylinders must first be pivoted out of the way. The trunnions of all the printing unit cylinders are supported in eccentric bushes, so that the desired positioning movements into and out of the position for printing can be executed in the appropriate sequence by rotating the eccentric bushes.